# Stored data for newform 1950.2.y.i, downloaded from the LMFDB on 19 April 2024. {"label": "1950.2.y.i", "space_label": "1950.2.y", "level": 1950, "weight": 2, "hecke_orbit": 9, "hecke_orbit_code": 36030446319962014, "dim": 8, "is_polredabs": true, "nf_label": "8.0.5308416.1", "trace_hash": 2291496957466221540, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[7, [4, 8, 20, 8, 22, 16, 14, 4, 1]]], "qexp_display": "q+(-1+\\zeta_{24}^{4})q^{2}-\\zeta_{24}^{2}q^{3}-\\zeta_{24}^{4}q^{4}+\\cdots", "char_order": 6, "char_parity": 1, "char_degree": 2, "char_conductor": 65, "char_orbit_label": "y", "char_is_real": false, "Nk2": 7800, "analytic_conductor": 15.570828394149675, "hecke_ring_index": 1, "level_radical": 390, "field_poly_is_cyclotomic": true, "field_poly_root_of_unity": 24, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.195", "prec": 17}, "analytic_rank_proved": true, "char_values": [1950, 6, [1301, 1327, 301], [6, 3, 5]], "hecke_ring_generator_nbound": 7, "inner_twist_count": 2, "level_primes": [2, 3, 5, 13], "conrey_indexes": [49, 199], "field_disc": 5308416, "field_disc_factorization": [[2, 16], [3, 4]], "field_poly": [1, 0, 0, 0, -1, 0, 0, 0, 1], "hecke_ring_index_factorization": [], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "7.454", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "233.403", "prec": 24}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "12857.405", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 4, "sato_tate_group": "1.2.3.c6", "trace_display": [-4, 0, 0, -4], "traces": [0, 8, -4, 0, -4, 0, 0, -4, 8, 4, 0, -12, 0, 0, 8, 0, -4, 0, -8, -12, 0, 0, 12, -12, 0, 0, 0, 0, -4, -4, 0, 0, -4, 8, 0, 0, 4, -16, 0, 0, 0, 0, 0, 24, 0, 0, 12, 32, 0, 16, 0, -8, 0, 0, 0, 0, -4, 0, -4, 12, 0, -16, -24, 4, 8, 0, -16, 24, 0, -4, 0, 60, 4, -24, -16, 0, 12, 0, 0, 8, 0, -4, 0, -8, 0, 0, 0, -12, -12, -24, 0, 8, 0, 4, -16, 0, 0, 0, 16, 0, 0, -44, 4, 0, 0, 0, -24, -12, 0, 0, 0, 24, 8, 0, 0, 0, 8, 0, 0, 0, 0, -8, 32, -20, 24, 0, 4, -24, -4, -8, 0, -40, 8, 0, 24, 0, 0, -36, 8, 12, 0, 24, 0, 8, -8, 0, 12, -12, 32, 0, 0, 0, -12, 0, -24, 0, 0, 0, -4, -4, 0, 0, -4, 12, 0, 0, 4, -20, 0, 0, 0, -12, -24, 24, 0, 0, 12, 24, 24, 12, 0, 0, 20, 0, -12, 0, 4, 8, -16, 0, 0, 12, 0, -12, 0, 0, -32, 44, 12, -20, 0, -24, -44, -16, 4, 0, 0, 0, 0, 0, 0, -4, 24, -8, 12, 0, 0, -12, -48, 24, 0, 24, 0, -24, -4, 0, 0, 32, 0, 0, 0, 4, -4, 0, 0, 0, -12, 0, 0, 0, 0, 60, 16, 0, -16, 0, 40, 12, 0, 24, 0, -12, -8, -24, 24, 0, -4, -48, 4, -32, 0, -8, 20, 108, 8, 0, 0, -4, -48, 52, 0, -12, 0, 8, 72, 0, -4, 96, -24, -24, 0, 0, -24, 12, -60, 0, 20, 0, 4, 8, 0, 0, 12, 8, 0, 0, -16, -8, 0, -52, 0, -48, -60, -12, 0, 0, 0, 72, 24, 12, 0, 8, 0, 0, -48, 0, -4, -24, -4, -60, 0, -28, 24, -36, 8, 0, -24, 40, 0, -36, 0, 72, 4, -32, -20, 0, 0, 0, 0, -32, 0, 28, 12, -56, 24, 0, 0, -108, 12, 24, 0, 0, 0, -44, -12, 0, 0, -8, 12, 0, 0, -40, 0, 0, -28, 0, -48, -204, 12, 0, 0, 12, -8, 144, -4, 0, 32, 72, 0, 120, 0, 0, -24, -28, 0, 0, -12, 24, 0, 104, 0, -112, 16, 60, 44, 0, -12, -48, 40, 0, 0, 72, 0, -16, 88, 0, 8, 60, -8, -36, 0, 0, 0, -36, 12, 0, 0, 0, 0, 44, 0, 0, -4, 16, 0, 0, 4, -40, 0, -20, 0, -36, 0, 36, 0, 0, 48, 120, -24, 16, 0, 32, 60, 0, -24, 0, -24, -8, -4, -84, 0, -12, 0, -16, -64, 0, 0, 64, 72, -4, 0, 48, 4, -16, -4, 0, 72, 0, 0, -112, 0, 0, 12, -56, 0, 0, 0, -24, 12, 0, 0, 100, 0, 4, -8, 0, 0, 68, -16, 0, 0, -68, -20, 0, -48, 0, -24, -96, -24, 0, 0, 36, 24, 12, 4, 0, 48, -4, 0, -12, 0, -20, 8, 0, 48, 0, 4, -48, 16, 16, 0, -112, 4, 0, 20, 0, -108, -80, -16, 28, 0, 12, 0, 4, 8, 0, 24, -24, -104, -48, 0, 0, 12, -24, 0, 0, 20, 0, -36, 16, 0, 0, -4, -4, 0, 0, 12, -64, 0, 80, 0, -24, -96, -24, 0, 0, -12, 8, 60, -36, 0, 40, -28, 0, -48, 0, 4, 24, 8, 0, 0, -24, -12, 4, -24, 0, -16, 96, 12, 0, 0, -12, -16, -8, -8, 0, 0, 0, -52, 88, 0, 16, 48, 48, 60, 0, 0, 36, 12, 24, 0, -4, 0, -48, -36, 0, 0, 32, 12, 0, 0, 4, -4, 0, 0, 0, -24, -12, 48, 0, 0, 0, 8, 0, 12, 0, 8, -56, 0, 60, 0, -28, 56, 16, -24, 0, -36, -12, -4, -40, 0, -72, 12, 60, 40, 0, 0, -12, 72, 12, 0, 144, 0, -24, -8, 0, 16, 228, 40, -84, 0, 0, 0, -60, -60, 0, 0, 0, 16, -40, 0, 0, 28, 68, 0, 0, 28, 32, 0, 48, 0, -24, -24, -24, 0, 0, -12, 88, -24, -16, 0, 128, 0, 0, -12, 0, -44, 96, -12, -24, 0, 4, -24, 4, 16, 0, -24, 60, 48, -20, 0, -36, -40, 24, 0, 0, 48, 0, 8, -8, 0, 100, 48, -128, 204, 0, 0, -168, 0, 12, 0, 36, 0, 16, 4, 0, 0, -4, -4, 0, 0, 12, -16, 0, -132, 0, 0, -240, -120, 0, 0, -36, 0, 96, 12, 0, 56, 8, 0, 156, 0, 4, 24, -16, -24, 0, 0, -84, -52, -72, 0, -192, 56, -12, 16, 0, -60, -84, -88, 12, 0, -48, 0, 24, 96, 0, -20, 132, 0, -132, 0, 0, -72, 36, 24, 0, 116, 0, -44, 60, 0, 0, 8, 20, 0, 0, 4, -60, 0, 28, 0, -120, -36, -72, 0, 0, 36, 8, -12, 32, 0, -32, 0, 0, -36, 0, 0, 8, 44, -156, 0, -68, -72, 44, 8, 0, -32, 0, -24, -16, 0, 108, 4, 128, -40, 0, -12, 0, 28, 48, 0, -40, 36, 40, 0, 0, 0, -108, 12, -48, 0, 112, 0, 0, -60, 0, 0, 40, 16, 0, 0, -44, -16, 0, -84, 0, 0, -144, 24, 0, 0, 12, 48, 36, 4, 0, 8, 88, 0, 144, 0, 32, 24, -24, 0, 0, -16, -96, 32, -88, 0, 104, 0, 12, 64, 0, -72, 20, 8, 0, 0, 132, 0, 52, -8, 0, 8, 0, 8, 0, 0, 0, -72, 12, 96, 0, 0, 0, 56, -28, 0, 0, 0, -72, 0, 0, 28, -32, 0, 80, 0, 96, 0, -72, 0, 0, -12, 56, 0, -16, 0, -160, 16, 0, -60, 0, 4, 192, -8, 84, 0, 20, 0, 32, -136, 0, 32, 176, 24, -28, 0, -48, -68, -160, -20, 0, -168, 0, 36, -128, 0, -36, 24, -104, 96, 0, 0, 72, 12, 24, 0, -48, 0, -132, -12, 0, 0, -48, 4, 0, 0, -12, -24, 0, -88, 0, -24, 0, 12, 0, 0, 48, 40, -120, -4, 0, 0, -108, 0, 36, 0, -64, -8, 44, 48, 0, 16, -48, -8, -72, 0, 0, 56, 12, 4, 0, 0, 16, -40, 80, 0, -96, 0, 0, 160, 0, 8, 84, -56, 0, 0, 0, -12, 108, 0, 0, 88, 0, -4, 72, 0, 0, 24, 20, 0, 0, 52, -16, 0, 52, 0, 108, -48, -36, 0, 0, 24, 184, 0, 8, 0, 32, -28, 0, -108, 0, -36, 264, 16, -36, 0, -12, 120, 136, 8, 0, 8, 20, -96, -76, 0, 108, 12, 8, -64, 0, 24, 0, 44, 0, 0, 60, 24, 40, 96, 0, 0, -108, 24, -108, 0, 12, 0, -4, -4, 0, 0, -24, -36, 0, 0, 16, -20, 0, 8, 0, 36, -348, 48, 0, 0, -108, -8, 204, -12, 0, -16, -20, 0, 12, 0, -4, 48, -84, 12, 0, 4, -36, 12, 200, 0, 96, 8, 156, 96, 0, -12, -92, 0, -20, 0, 60, 0, 0, 32, 0, 4, 48, 16, -72, 0, 0, 0, 108, 24, 0, 104, 0, -44, 148, 0, 0, 16, 40, 0, 0, -24, -56, 0, 124, 0, -96, 12, -192, 0, 0, -12, 16, -24, 76, 0, -168, -88, 0, 0, 0, -48, 136, -36, -96, 0, 40, -24, 36, -64, 0, -24, -8, 96, -4, 0, -24, 4, -128, -4, 0, 48, 0, 0, -152, 0, -12, 24, -128, 12, 0, 0, -144, 48, 0, 0, -104, 0, 64, -4, 0, 0, 68, 12, 0, 0, -64, -4, 0, 16, 0, 60, -288, -60, 0, 0, 12, 56, -204, -28, 0, -32, 28, 0, 24, 0, 64, 72, -44, 12, 0, -4, -36, 20, -48, 0, 80, 36, 144, 12, 0, -60, 32, -80, -32, 0, -48, 0, -8, 24, 0, -36, 0, -24, -216, 0, 0, -144, -12, -72, 0, -60, 0, 4, -92, 0, 0, 16, -96, 0, 0, -20, 8, 0, 104, 0, 0, -180, -216, 0, 0, 60, -48, 60, -12, 0, -8, 0, 0, -168, 0, 16, 224, -40, -60, 0, -16, 12, 80, -56, 0, -136, 108, -12, -116, 0, 84, 28, 24, 32, 0, -24, 0, -36, 16, 0, -32, 24, 88, 24, 0, 0, 84, 108, 60, 0, -48, 0, -36, -44, 0, 0, -8, -16, 0, 0, -4, -64, 0, 0, 0, 60, -24, 12, 0, 0, -60, 88, -48, -48, 0, 24, -52, 0, 0, 0, 28, -8, 116, 24, 0, 4, 24, -8, 192, 0, -8, 12, 276, 60, 0, -48, -8, 40, 0, 0, 204, 0, 124, 80, 0, -12, 132, 0, 24, 0, 0, -48, -24, -180, 0, 20, 0, 4, -124, 0, 0, 100, 0, 0, 0, 64, -12, 0, 80, 0, -72, -12, -96, 0, 0, 0, 32, -12, 112, 0, 120, 12, 0, -12, 0, 16, 88, 4, 132, 0, -4, -144, 4, 8, 0, 8, 0, 60, -96, 0, 96, 12, -40, -16, 0, 48, 0, 60, -40, 0, 60, 0, -88, 240, 0, 0, -288, 0, 180, 0, 0, 0, 32, 0, 0, 0, 0, 12, 0, 0, -48, -28, 0, -136, 0, 0, -144, -156, 0, 0, 96, -8, 168, -12, 0, 32, -64, 0, 72, 0, 16, 0, 4, 84, 0, -52, 24, 36, 152, 0, 72, 96, 0, 56, 0, 12, -108, -32, -80, 0, -276, 0, -152, 168, 0, 44, 72, -24, -144, 0, 0, 48, 144, 12, 0, 60, 0, -48, 92, 0, 0, -20, 12, 0, 0, 0, -8, 0, -52, 0, -72, 24, -60, 0, 0, -36, 72, -24, -32, 0, 24, -100, 0, -72, 0, -44, 104, 60, -48, 0, -64, 24, -24, -16, 0, -40, -12, -60, 0, 0, 24, 4, 96, -60, 0, 36, 0, -8, -40, 0, -48, 120, -40, 36, 0, 0, -48, 0, -228, 0, -224, 0, -48, -4, 0, 0, 156, 32, 0, 0, 64, 16, 0, 0, 0, 12, -108, 36, 0, 0, -48, 0, -84, -4, 0, -88, 16, 0, 156, 0, 40, 136, 4, 72, 0, 44, -36, -4, -24, 0, 168, 16, -240, 0, 0, 24, -92, 32, 80, 0, 0, 0, 72, -8, 0, -64, 84, 80, -96, 0, 0, 12, -84, 60, 0, -8, 0, -24, -12, 0, 0, -40, 120, 0, 0, -20, 36, 0, 48, 0, 72, -36, -72, 0, 0, -12, -24, 48, 28, 0, -208, -32, 0, -48, 0, 0, 40, -60, -24, 0, 72, 24, -84, -80, 0, -32, 40, 84, 8, 0, 132, -44, 8, -16, 0, -72, 0, 24, -136, 0, -28, 0, 88, 144, 0, 0, 84, -24, 0, 0, -92, 0, -104, -24, 0, 0, 100, 4, 0, 0, 20, -4, 0, -92, 0, 84, -12, -144, 0, 0, -84, -64, -96, -12, 0, 48, -92, 0, -24, 0, 168, 32, 152, 96, 0, 32, 168, 44, -88, 0, 24, -52, 24, 0, 0, -12, -8, -128, 116, 0, -108, 0, 104, -40, 0, -4, 216, 0, -144, 0, 0, -132, 48, -48, 0, -104, 0, 4, 32, 0, 0, 8, 64, 0, 0, -4, 48, 0, -8, 0, 96, -72, 12, 0, 0, -12, 56, -96, 24, 0, 152, 0, 0, -96, 0, 56, 80, -28, -36, 0, 0, -48, 44, 0, 0, 144, 28, -12, -200, 0, 36, 28, -48, -32, 0, 0, 0, -112, -8, 0, -164, -96, -144, 0, 0, 0, -84, 24, 144, 0, -56, 0, 68, -28, 0, 0, -4, -16, 0, 0, -32, 80, 0, -116, 0, 12, -276, 60, 0, 0, -60, -8, 96, -96, 0, 16, -60, 0, -84, 0, 36, -40, -48, 0, 0, 32, 36, 68, 312, 0, 320, -16, -12, 176, 0, -24, -48, 56, 48, 0, -84, 0, -156, 136, 0, 80, 72, 40, -204, 0, 0, 168, 144, 36, 0, 12, 0, 64, 72, 0, 0, -36, -8, 0, 0, 52, -152, 0, 84, 0, 36, 24, 168, 0, 0, -12, -208, -24, 176, 0], "weight_parity": 1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": false, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 65, 12, 1, 6, 0]], "char_orbit_index": 25, "prim_orbit_index": 12, "minimal_twist": "1950.2.bc.e", "char_is_minimal": false, "conrey_index": 49, "id": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, -1, 0], [0, 1, 0, -1, -1, -1, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, -2, -1, -1, -1, 0, 1], [0, 0, 0, 0, 0, 0, 1, 0], [0, -3, 0, 0, 0, 4, 0, 0], [1, 0, 0, 0, 0, 1, 0, -1], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, -3, 1, -3, 0, 3, -1, 3], [-1, 0, 0, 0, 0, 0, 0, 0], [-2, 2, 0, 1, 1, -1, 0, -2], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, 0, 0, 1, 1], [2, 1, 2, 0, -1, 0, -2, -1], [-1, 1, 1, 4, -1, 3, 0, -3], [0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, -3, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0], [-1, -1, 0, 1, 1, 0, 0, 0], [-1, 4, 1, 1, 1, -5, -2, -5], [0, 0, 0, 0, 0, 0, 0, 0], [-2, 3, 0, -3, 4, 2, 1, 5], [0, 0, 0, 0, -1, 0, 0, 0], [0, 1, 1, 0, 2, 0, 1, 1], [0, 0, 0, 0, 0, -3, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, -1, 0, 0, 0], [-4, 3, -2, -5, 4, 2, 4, 2], [1, -1, 0, 1, -2, 2, 0, 1], [0, 0, 0, 3, 0, 0, 0, -4], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 5, -3, 0, -4, 0, 4], [0, -1, -1, 0, 0, 1, 0, -1], [4, -3, 1, -5, -2, 5, -1, 3], [-1, -1, 0, 1, 2, 1, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [2, -4, -1, -1, -1, 1, 1, 4], [4, 3, -4, 3, 0, 1, 2, -4], [0, 0, 1, 0, 0, 0, -1, 0], [4, -2, 1, 2, -4, 0, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 3, 0, 3, 0, 0, 0, -3], [0, 4, 0, 0, 0, -1, 0, 0], [-2, 1, 0, -1, 4, -2, -1, -1], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, -1, -1, -1, 0, 1], [0, -2, 2, -2, 0, 1, -1, 1], [0, 1, 1, 4, -1, 4, 1, 1], [2, 6, -3, 4, -1, -4, 3, -6], [0, 0, 0, 0, 0, 0, 0, 0], [0, 3, -4, -3, -4, -3, -4, 3], [-2, -5, -1, -2, -2, 3, 0, -3], [1, 1, 0, -1, -1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -1, -2, -1, 0, 1, 1, 0], [6, 4, 2, -4, -6, 0, -4, 0], [0, 3, -1, 3, 0, 0, 0, 0], [0, -3, 1, -1, -1, -1, 1, -3], [0, 0, 0, 0, 0, 0, 0, 0], [10, 4, 1, 1, -5, -1, -1, -4], [0, 0, 0, 0, 1, 0, 0, 0], [-3, 0, -4, 0, 0, 4, 2, -4], [0, -5, -2, 3, -4, 3, -2, -5], [0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 0, -2, 1, -1, 0, 1], [-2, -1, 0, 1, 4, 2, 1, 1], [0, 0, 0, 1, 0, 0, 0, 3], [1, 6, 0, 6, 0, -3, 0, -3], [0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0, 0, 0], [0, 3, -5, -1, 0, 1, 5, -3], [-1, 1, -4, 1, 0, 3, 2, -4], [0, 0, 1, 1, 0, -1, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0], [-2, -2, 0, 2, 4, -3, 1, -5], [-2, -5, 1, -4, 1, 4, -1, 5], [-1, 0, -2, -1, -1, -1, 0, 1], [-2, -1, 1, 5, -2, 6, 0, -6], [0, 0, 0, 0, 0, 0, 0, 0], [3, 4, 1, 0, -4, -1, 3, 0], [-1, 3, 0, -3, 2, -4, -1, -1], [1, 5, 2, -3, -1, -2, -4, -2], [-4, -4, 2, 1, 4, 3, -4, 3], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0], [0, 8, -1, -2, 0, -2, -1, 8], [0, 2, 1, -2, 4, -2, 1, 2], [1, 1, 0, -1, -2, -1, -2, 0], [0, 0, 0, 0, 0, 0, 0, 0]]}